If the Leafs' won the cup this year Matthews would be around 22 years 9 months. Marner would be 23, Nylander 24, Rielly 26 and Tavares 29. They are not as young as you are letting on.
As to how many cores that are that young have won the cup? The three big cup winners of the past decade are Pittsburgh, Chicago and LA who won 8 cups over the past 11 years.
Crosby was 21, Letang and Malkin 22 and Fleury 24 when they won their first cup. They had gone to the finals the year before.
Kane was 21, Toews had just turned 22 and Keith was 26 (and most of the team was younger than him) when they won their first cup. They had made it to the third round the year before.
Doughty was 22 and Kopitar was 24 when they won their first cup.
The problems that the Leafs' have this season are many but they have nothing to do with their age.
The truly great players peak early.
Ovechkin peaked at age 22 -- 65 goals, 122 points. He hasn't done that before or since. In fact, Ovi scored 100 points four times by age 24. Since he turned 25 he hasn't done that even once.
Bobby Orr was 22 in 1970 when he won the Stanley Cup, the Conn Smythe, the Art Ross, the Hart and the Norris trophies all at once. Nobody has done that before or since.
Wayne Gretzky was 21 when he scored 92 goals and 212 points. He did break his own points record with 215 at age 25, but no one has ever matched the 92 goals of the 21 y.o. Gretzky.
Teemu Selanne scored 76 goals and 126 points as a 22 y.o. rookie. He never came close to that again.
In 1944-45 a 23 y.o. Maurice Richard set the standard of 50 goals in 50 games, sandwiched between Stanley Cup wins in 1943-44 and '45-46 for a Habs franchise that had been in the dumps, not winning a Cup since 1931.
The Leafs core is not too young to perform well. In fact, these are the years that we should expect to see the peak performances of those among them that have true greatness. That could be one or more, or maybe none. Seeing is believing.